O'Neill, who is one of three senior appointments announced by Tesco this week, told The Grocer she would look at ways to bring down costs in the Republic of Ireland.
She joined Tesco Ireland last week from her previous role as category director for health and beauty. Her first move was to invest €21m (£20m) in cutting the price of clothing in the Republic by 7%. The initiative matches the prices pound for euro, so a £10 jumper in Northern Ireland would now cost €10 in the Republic.
O'Neill told The Grocer that the economy in Ireland was "very tough" and she would look at why prices were higher in the Republic than in the UK.
The price cuts on clothing were possible because of the weakness of sterling, which allowed Tesco Ireland to buy more cheaply, she said. "We noticed some people were prepared to travel north to get a better deal, so given that we have such a strong business in the UK, we thought we would leverage our strengths there and bring sterling-euro parity to our customers," she added.
"I will be looking at our overall efficiencies, comparing them with our UK operations and asking why there is a difference and whether it has to be that way," she said. "I am going in, analysing, getting the detail and seeing what emerges."
Meanwhile, Richard Jones has joined Tesco as UK commercial director for non-food hard lines following a spell on gardening leave from Sainsbury's.
Jones, who was behind the launch of Sainsbury's Tu clothing brand, left the retailer in June last year.
His new role is currently occupied by Chris Holmes, who is moving to a similar role in Tesco's European business.
Anne Gardener, who has spent five years as trading director at Argos, is also to join Tesco. She will be responsible for the development of the home category across the Tesco Group in her new role.